Measuring apparatus

ABSTRACT

The present invention provides a measuring apparatus for measuring an absolute distance between a reference surface an d a test surface, including a phase detection unit configured to detect an interference signal between light reflected by the reference surface and light reflected by the test surface, and detect, from the interference signal, a phase corresponding to an optical path length between the reference surface and the test surface, and a processing unit configured to perform processing of obtaining the absolute distance by controlling the phase detection unit so as to detect the phase corresponding to the optical path length between the reference surface and the test surface for each of a first reference wavelength and a second reference wavelength while changing the wavelength of light to be emitted by a first light source continuously from the first reference wavelength to the second reference wavelength.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a measuring apparatus for measuring theabsolute distance between a reference surface and a test surface.

2. Description of the Related Art

As an apparatus for measuring the absolute distance between a referencesurface and a test surface, a wavelength scanning type light waveinterference measuring apparatus is known. The accuracy of absolutedistance measurement by wavelength scanning is generally low. For thisreason, the measurement accuracy is improved by combining relativedistance measurement using a fixed wavelength. Hence, the main accuracyfactors of the wavelength scanning type light wave interferencemeasuring apparatus are the accuracy of wavelength scanning (wavelengthscanning amount), the accuracy of the fixed wavelength, and themeasurement accuracy of a phase when measuring the relative distance.

FM heterodyne, an absolute distance measurement scheme using wavelengthscanning, measures the intensity of a single interference signal, andcalculates the absolute distance from a change in the intensity of theinterference signal caused during wavelength scanning. For example,Japanese Patent No. 2725434 discloses a technique of guaranteeing thescanning amount of an atmospheric wavelength using a referenceinterferometer (that is, based on the length of the referenceinterferometer) and also guaranteeing a fixed wavelength using awavelength reference such as an etalon or gas cell in FM heterodyne.

As a technique of measuring the absolute distance more accurately thanFM heterodyne, Japanese Patent No. 2810956 discloses a technique ofmeasuring a phase by obtaining a Lissajous' waveform from theintensities of two interference signals with a phase shift of 90°. InJapanese Patent No. 2810956, the scanning amount of an atmosphericwavelength is guaranteed by using a common reference interferometer forthe wavelength scanning amount and the fixed wavelength. In addition,the fixed wavelength is controlled to make the atmospheric wavelengthconstant, thereby guaranteeing the variation in the refractive index ofatmosphere.

However, because of a low phase measurement accuracy, the conventionallight wave interference measuring apparatus cannot attain a sufficientmeasurement accuracy (that is, required measurement accuracy) even bycombing relative distance measurement. Furthermore, when the phasemeasurement accuracy is low, the wavelength scanning amount needs to belarger to combine absolute distance measurement and relative distancemeasurement. This adds constraints on choice of a light source in theinterferometer.

The techniques disclosed in Japanese Patent Nos. 2725434 and 2810956need a reference interferometer. Hence, the arrangement of the lightwave interference measuring apparatus becomes complex, and themeasurement accuracy is reduced due to the variation in the length ofthe reference interferometer used as a reference.

SUMMARY OF THE INVENTION

The present invention provides a technique of accurately measuring theabsolute distance between the reference surface and a test surface usinga simple arrangement.

According to one aspect of the present invention, there is provided ameasuring apparatus for measuring an absolute distance between areference surface and a test surface, including a wavelength referenceelement configured to set a wavelength of light to be emitted by a firstlight source to one of a first reference wavelength that is a knownvacuum wavelength and a second reference wavelength that is a knownvacuum wavelength different from the first reference wavelength, apolarizing beam splitter configured to split the light from the firstlight source into light having a first polarization direction and lighthaving a second polarization direction perpendicular to the firstpolarization direction, make the light having the first polarizationdirection enter the reference surface, and make the light having thesecond polarization direction enter the test surface, a refractive indexdetection unit configured to detect a group index in a space between thereference surface and the test surface, a phase detection unitconfigured to detect an interference signal between the light having thefirst polarization direction and reflected by the reference surface andthe light having the second polarization direction and reflected by thetest surface, and detect, from the interference signal, a phasecorresponding to an optical path length between the reference surfaceand the test surface, and a processing unit configured to performprocessing of obtaining the absolute distance by controlling the phasedetection unit so as to detect the phase corresponding to the opticalpath length between the reference surface and the test surface for eachof the first reference wavelength and the second reference wavelengthwhile changing the wavelength of light to be emitted by the first lightsource continuously from the first reference wavelength to the secondreference wavelength by using the wavelength reference element, whereinletting λ₁ be the first reference wavelength, λ₂ be the second referencewavelength, φ₁ be the phase detected by the phase detection unit at thefirst reference wavelength, φ₂ be the phase detected by the phasedetection unit at the second reference wavelength, M be the number ofphase jumps that occur when the wavelength of light to be emitted by thefirst light source is continuously changed from the first referencewavelength to the second reference wavelength, Λ₁₂ be a syntheticwavelength of the first reference wavelength and the second referencewavelength represented by λ₁·λ₂/|λ₁−λ₂|, n_(g) be the group indexdetected by the refractive index detection unit, and k be the number oftimes the test surface reflects the light having the second polarizationdirection, the processing unit obtains the absolute distance D₁ by

$D_{1} = {\frac{1}{2\;{k \cdot n_{g}}}\left( {M + \frac{\phi_{2} - \phi_{1}}{2\;\pi}} \right){\Lambda_{12}.}}$

Further aspects of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view showing the arrangement of a measuringapparatus according to the first embodiment of the present invention.

FIG. 2 is a flowchart for explaining measurement processing of themeasuring apparatus shown in FIG. 1.

FIGS. 3A to 3C are views for explaining steps S204 and S208 of theflowchart shown in FIG. 2.

FIG. 4 is a schematic view showing the arrangement of a measuringapparatus according to the second embodiment of the present invention.

FIG. 5 is a view showing the detailed arrangement of a phase detectionunit of the measuring apparatus shown in FIG. 4.

FIG. 6 is a flowchart for explaining measurement processing of themeasuring apparatus shown in FIG. 4.

FIG. 7 is a schematic view showing the arrangement of a measuringapparatus according to the third embodiment of the present invention.

FIG. 8 is a flowchart for explaining measurement processing of themeasuring apparatus shown in FIG. 7.

FIG. 9 is a schematic view showing the arrangement of a measuringapparatus according to the fourth embodiment of the present invention.

FIGS. 10A to 10C are graphs showing the transmission spectrum of a gascell, the transmission spectrum of a Fabry-Perot etalon, and thespectrum of light emitted by each of two light sources in the measuringapparatus shown in FIG. 9.

FIG. 11 is a flowchart for explaining measurement processing of themeasuring apparatus shown in FIG. 9.

DESCRIPTION OF THE EMBODIMENTS

Preferred embodiments of the present invention will be described belowwith reference to the accompanying drawings. Note that the samereference numerals denote the same members throughout the drawings, anda repetitive description thereof will not be given.

<First Embodiment>

FIG. 1 is a schematic view showing the arrangement of a measuringapparatus 1 according to the first embodiment of the present invention.The measuring apparatus 1 is a light wave interference measuringapparatus for measuring the absolute distance between a referencesurface and a test surface. As shown in FIG. 1, the measuring apparatus1 includes a light source 102, beam splitters 104 a and 104 b, awavelength shift unit 106, a Fabry-Perot etalon 108 serving as awavelength reference element, and an intensity detection unit 110. Themeasuring apparatus 1 also includes a light source control unit 112,non-polarizing beam splitter 114, reference signal detection unit 116,polarizing beam splitter 118, measurement signal detection unit 120,environment detection unit 122, and processing unit 124.

As will be described later, the measuring apparatus 1 stabilizes ameasurement wavelength (for example, vacuum wavelength) for a long term,and obtains the refractive index of a gas near the test surface, therebyaccurately measuring the absolute distance between the reference surfaceand the test surface. In addition, the test surface and the referencesurface reflect light components whose polarization directions areperpendicular to each other, thereby implementing phase detection byaccurate heterodyne detection.

Light emitted, as linearly polarized light, by the light source 102serving as a first light source is split (branched) into three lightcomponents via the two beam splitters 104 a and 104 b. The light source102 is a wavelength variable light source capable of continuouslychanging the wavelength in the wavelength band (vacuum wavelength) to beused for the measurement. In this embodiment, an easily andinexpensively available DFB-DL (Distributed Feed-Back Diode Laser)mass-produced for optical communication is used as the light source 102.However, the light source 102 is not limited to the DFB-DL, and anexternal cavity diodelaser or fiber laser may also be used.

Out of the two light components split by the beam splitter 104 a, thelight component transmitted through the beam splitter 104 a enters thenon-polarizing beam splitter 114, and the light component reflected bythe beam splitter 104 a enters the beam splitter 104 b. Out of the twolight components split by the beam splitter 104 b, the light componentreflected by the beam splitter 104 b enters the wavelength shift unit106, and the light component transmitted through the beam splitter 104 benters the Fabry-Perot etalon 108.

In this embodiment, the wavelength shift unit 106 includes a shifter 106a formed from an acousto-optic device or the like, and a polarizationrotation unit 106 b formed from a wave plate or the like. The shifter106 a shifts the frequency (incident wavelength) of incident light by aknown (predetermined) frequency dν. The polarization rotation unit 106 bchanges the polarization direction of light that has passed through theshifter 106 a (more specifically, rotates the light by 90°), and exits alight component having a polarization direction perpendicular to that ofthe incident light. The light that has exited from the wavelength shiftunit 106 enters the non-polarizing beam splitter 114.

The intensity detection unit 110 detects the intensity (etalontransmission intensity) of the light transmitted through the Fabry-Perotetalon 108. Based on the etalon transmission intensity detected by theintensity detection unit 110, the light source control unit 112 controlsthe wavelength of light to be emitted by the light source 102. Forexample, the light source control unit 112 modulates the temperature ofthe light source 102 or the current to be supplied to the light source102, thereby controlling (adjusting) the wavelength of light to beemitted by the light source 102.

Note that for the transmission spectrum of the Fabry-Perot etalon 108,the absolute value of the vacuum wavelength needs to be guaranteed. Inthis embodiment, a vacuum medium etalon with a guaranteed transmissionspectrum interval is used as the Fabry-Perot etalon 108. The vacuummedium etalon can easily guarantee the absolute value of the vacuumwavelength because there is neither the refractive index nor dispersionof the internal medium. If low thermal expansion glass or the like isused as the material of the etalon, the expansion coefficient for thetemperature can be reduced so that a wavelength reference element thatis stable for a long term can be implemented. However, the Fabry-Perotetalon 108 is not limited to the vacuum medium etalon, and an air gapetalon or solid etalon may be used. In this case, the internalrefractive index and dispersion need to be guaranteed by, for example,measuring the temperature of the etalon. Alternatively, the etalon maybe combined with a gas cell to obtain a more stable referencewavelength.

The light component transmitted through the beam splitter 104 a and thattransmitted through the wavelength shift unit 106 merge into a commonoptical path again at the non-polarizing beam splitter 114 which splitsthe light into two light components again. One of the light componentssplit by the non-polarizing beam splitter 114 enters the referencesignal detection unit 116.

The reference signal detection unit 116 detects, as the interferencesignal between the light transmitted through the beam splitter 104 a andthat transmitted through the wavelength shift unit 106, a beat signalcorresponding to the frequency difference between the light components.The reference signal detection unit 116 includes a polarizer, anddetects the interference signal by extracting a light component having acommon polarization direction between the light transmitted through thebeam splitter 104 a and that transmitted through the wavelength shiftunit 106. If the accuracy needs to be higher, the reference signaldetection unit 116 may perform difference detection by generating aninterference signal that is different by 180° by combining the polarizerwith a wave plate. The interference signal generated by the referencesignal detection unit 116 will be referred to as a reference signalhereinafter.

The other of the light components split by the non-polarizing beamsplitter 114 enters the polarizing beam splitter 118. The polarizingbeam splitter 118 has a function of splitting the light from the lightsource 102 into a light component having a first polarization directionand a light component having a second polarization directionperpendicular to the first polarization direction. In this embodiment,the polarizing beam splitter 118 passes the light component transmittedthrough the beam splitter 104 a, and reflects the light componenttransmitted through the wavelength shift unit 106.

The light reflected by the polarizing beam splitter 118 is reflected bya reference surface RS. The light is reflected by the polarizing beamsplitter 118 again, and enters the measurement signal detection unit120. The reference surface RS is formed from a corner cube having aplurality of reflecting surfaces, and fixed to a reference structureserving as the reference of distance measurement together with thepolarizing beam splitter 118. The light reflected by the referencesurface RS will be referred to as reference light hereinafter.

The light transmitted through the polarizing beam splitter 118 isreflected by a test surface TS. The light passes through the polarizingbeam splitter 118 again, and enters the measurement signal detectionunit 120. The test surface TS is formed from a corner cube, like thereference surface RS, and fixed to the target object (test object) ofdistance measurement. The light reflected by the test surface TS will bereferred to as test light hereinafter.

In this embodiment, the interferometer in the measuring apparatus 1 isdesigned such that the optical path difference between the referencelight and the test light corresponds to one roundtrip (that is, thenumber of times the test surface TS reflects the test light is one).However, the interferometer may be designed in a different way. Forexample, the interferometer may be designed by inserting a λ/4 plate ineach of the optical paths of the reference light and test light andarranging a corner cube configured to reflect one-roundtrip light sothat the optical path difference between the reference light and thetest light corresponds to two roundtrips.

The measurement signal detection unit 120 has the same arrangement asthat of the reference signal detection unit 116, and detects theinterference signal between the reference light and the test light. Theinterference signal detected by the measurement signal detection unit120 will be referred to as a measurement signal hereinafter. Themeasurement signal is a beat signal corresponding to the frequencydifference between the reference light and the test light, like thereference signal. However, the phase of the interference signal isdifferent from that of the reference signal because of the optical pathdifference between the reference light and the test light.

The polarizing beam splitter 118 capable of splitting light inaccordance with the polarization direction is used as a beam splittingelement of the measuring apparatus 1 for measuring the absolute distancebetween the reference surface and the test surface. This allows asplitting of light reflected by each of the reference surface and thetest surface in accordance with the polarization direction. Hence, aslight frequency shift difference is added between the two lightcomponents whose polarization directions are perpendicular to eachother. This enables heterodyne detection to be performed between thereference surface and the test surface, and thus implement accuratephase detection.

The environment detection unit 122 is arranged near the test surface TSto measure the environment in the space near the test surface TS, andmore specifically, between the reference surface RS and the test surfaceTS. In this embodiment, the environment detection unit 122 functions asa refractive index detection unit which detects the group index in thespace (that is, atmosphere) between the reference surface RS and thetest surface TS. The environment detection unit 122 includes, forexample, a thermometer that detects the temperature of a gas in thespace between the reference surface RS and the test surface TS, and abarometer that detects the atmospheric pressure in the space between thereference surface RS and the test surface TS. The temperaturesensitivity and atmospheric pressure sensitivity of the refractive indexof the atmosphere are 1 ppm/C.° and 0.3 ppm/hPa, respectively. Hence,even when the environment detection unit 122 is formed from relativelycheap thermometer and barometer, a refractive index for about 0.1 ppmcan easily be guaranteed.

The processing unit 124 performs processing for obtaining the absolutedistance between the reference surface RS and the test surface TS usingthe reference signal detected by the reference signal detection unit116, the measurement signal detected by the measurement signal detectionunit 120, and the refractive index detected by the environment detectionunit 122. In addition, the processing unit 124 controls the wavelengthof light to be emitted by the light source 102 via the light sourcecontrol unit 112.

In the measuring apparatus 1 of this embodiment, one interferometer isarranged for one light source 102. However, a plurality ofinterferometers may be arranged for one light source 102. Morespecifically, light is split (branched) between the non-polarizing beamsplitter 114 and the polarizing beam splitter 118, and an interferometeris arranged for each light component. In general, the refractive index(atmospheric refractive index) near the test optical path of eachinterferometer changes depending on the arrangement position of theinterferometer. However, when the refractive index is detected for eachinterferometer, the refractive index can be corrected for eachinterferometer. In this arrangement, since one light source suffices fora plurality of measurement axes (interferometers), the measuringapparatus for measuring the absolute distance between the referencesurface and the test surface can be implemented while suppressing cost.

Measurement processing (that is, processing of causing the processingunit 124 to obtain the absolute distance between the reference surfaceRS and the test surface TS) of the measuring apparatus 1 will bedescribed with reference to FIG. 2. The measurement processing of themeasuring apparatus 1 is divided into order-of-interferencedetermination processing in steps S204 to S214 and relative distancemeasurement processing in steps S216 to S220.

In step S202, it is determined whether or not to executeorder-of-interference determination processing. For example, immediatelyafter the start of absolute distance measurement or when the past phasedetection history is lost by, for example, shielding light from thelight source 102 (that is, relative distance measurement processingcannot be maintained), order-of-interference determination processingneeds to be executed. Note that whether or not to executeorder-of-interference determination processing is automaticallydetermined by the processing unit 124. Upon determining to executeorder-of-interference determination processing, the process advances tostep S204. If it is determined not to execute order-of-interferencedetermination processing, the process advances to step S216.

In step S204, the wavelength of light to be emitted by the light source102 is set to a first reference wavelength λ₁ (that is, wavelengthstabilization control at the first reference wavelength λ₁ starts). Thefirst reference wavelength λ₁ will be explained with reference to FIGS.3A and 3B. FIG. 3A shows the transmission spectrum of the Fabry-Perotetalon 108. FIG. 3B shows the spectrum of light emitted by the lightsource 102. As shown in FIG. 3A, the Fabry-Perot etalon 108 has atransmission characteristic periodical at a uniform frequency intervalFSR, and the absolute value of the vacuum wavelength is guaranteed, asdescribed above. As the first reference wavelength λ₁, one of thetransmission spectra of the Fabry-Perot etalon 108 is used. In otherwords, the wavelength of light to be emitted by the light source 102 isstabilized with respect to the transmission spectrum of the Fabry-Perotetalon 108 corresponding to the first reference wavelength λ₁. Note thatwavelength stabilization is performed by causing the light sourcecontrol unit 112 (processing unit 124) to control the light source 102such that the intensity detection unit 110 detects a predeterminedetalon transmission intensity. Note that if there is influence of thevariation in the incident light amount on the Fabry-Perot etalon 108,the incident light amount is detected, and correction is performed tomake the incident light amount constant (that is, not to vary theincident light amount).

In step S206, a phase φ₁ at the first reference wavelength λ₁ isdetected. Detecting a phase means detecting the phase difference betweenthe reference signal and the measurement signal. Hence, the processingunit 124 detects the phase of the reference signal and that of themeasurement signal using a phase meter, and obtaining the differencebetween them, thereby obtaining the phase φ₁ at the first referencewavelength λ₁. That is, the reference signal detection unit 116,measurement signal detection unit 120, and processing unit 124 functionas a phase detection unit that detects, from the interference signals, aphase corresponding to the optical path length between the referencesurface RS and test surface TS.

The phase at the first reference wavelength λ₁ will be explained here.Let L₁ be the optical path difference between the test light and thereference light from the light source 102 to the non-polarizing beamsplitter 114, and 2n(λ)D be the optical path difference between the testlight and the reference light from the non-polarizing beam splitter 114to the measurement signal detection unit 120. Note that n(λ) is therefractive index of the optical path of the test light, and D is theabsolute distance between the reference surface RS and the test surfaceTS. In this case, a reference signal I_(ref) and a measurement signalI_(test) are given by

$\begin{matrix}\left\{ \begin{matrix}{I_{ref} = {I_{0}{\cos\left( {2\;{\pi\left( {{d\;{vt}} + \frac{L_{1}}{\lambda_{1}}} \right)}} \right)}}} \\{I_{test} = {I_{0}{\cos\left( {2\;{\pi\left( {{d\;{vt}} + \frac{L_{1}}{\lambda_{1}} + \frac{2\;{n\left( \lambda_{1} \right)}D}{\lambda_{1}}} \right)}} \right)}}}\end{matrix} \right. & (1)\end{matrix}$

Referring to equations (1), the phase φ₁ at the first referencewavelength λ₁ detected in step S206 is given by

$\begin{matrix}{\phi_{1} = {2\;{\pi \cdot {{mod}\left( {\frac{2\;{n\left( \lambda_{1} \right)}D}{\lambda_{1}},1} \right)}}}} & (2)\end{matrix}$where mod(u,k) is the remainder of a first argument u for a secondargument k.

In step S208, the number of phase jumps is measured while continuouslychanging (scanning) the wavelength of light to be emitted by the lightsource 102 from the first reference wavelength λ₁ to a second referencewavelength λ₂ (that is, canceling wavelength stabilization control atthe first reference wavelength λ₁). Note that one of the transmissionspectra of the Fabry-Perot etalon 108 is used as the second referencewavelength λ₂, like the first reference wavelength λ₁.

Note that step S208 can also be regarded as a process of measuring acumulative phase generated by continuously changing the first referencewavelength λ₁ to the second reference wavelength λ₂. As the wavelengthof light emitted by the light source 102 changes from the firstreference wavelength λ₁ to the second reference wavelength λ₂ (FIG. 3B),the phase monotonously changes, as shown in FIG. 3C. Since the range ofphases detectable by the phase meter is ±π, phase jump occurs outsidethe range of ±π. Measuring the cumulative phase corresponds to countingphase jumps. The number of phase jumps measured in step S208 will berepresented by M hereinafter.

In step S210, when the wavelength of light to be emitted by the lightsource 102 has changed from the first reference wavelength λ₁ to thesecond reference wavelength λ₂, wavelength stabilization control at thesecond reference wavelength λ₂ starts. In other words, the wavelength oflight to be emitted by the light source 102 is stabilized with respectto the transmission spectrum of the Fabry-Perot etalon 108 correspondingto the second reference wavelength λ₂.

In step S212, a phase φ₂ at the second reference wavelength λ₂ isdetected. The phase φ₂ at the second reference wavelength λ₂ detected instep S212 is given by

$\begin{matrix}{\phi_{2} = {2\;{\pi \cdot {{mod}\left( {\frac{2\;{n\left( \lambda_{2} \right)}D}{\lambda_{2}},1} \right)}}}} & (3)\end{matrix}$

Referring to equations (2) and (3), the number M of phase jumps is givenby

$\begin{matrix}\left\{ \begin{matrix}{M = {\frac{2\;{n_{g}\left( {\lambda_{1},\lambda_{2}} \right)}D}{\Lambda_{12}} - \left( {\phi_{2} - \phi_{1}} \right)}} \\{\Lambda_{12} = \frac{\lambda_{1}\lambda_{2}}{{\lambda_{1} - \lambda_{2}}}}\end{matrix} \right. & (4)\end{matrix}$where Λ₁₂ is the synthetic wavelength of the first reference wavelengthλ₁ and the second reference wavelength λ₂ represented by λ₁·λ₂/|λ₁−λ₂|.Note that as indicated by equations (4), the number M of phase jumpscorresponds to the order of interference of the synthetic wavelengthΛ₁₂, and will therefore be referred to as the order M of interference ofthe synthetic wavelength. In addition, n_(g)(λ₁,λ₂) is the group indexfor the wavelengths λ₁ and λ₂.

In step S214, an order N₁₂ of interference (phase change amount) at thesecond reference wavelength λ₂ is calculated. First, using the syntheticwavelength Λ₁₂, a first absolute distance D₁ is obtained by

$\begin{matrix}{D_{1} = {\frac{\Lambda_{12}}{2\;{n_{g}\left( {\lambda_{1},\lambda_{2}} \right)}}\left( {M + \frac{\phi_{2} - \phi_{1}}{2\;\pi}} \right)}} & (5)\end{matrix}$In this embodiment, since the number k of times the test light isreflected by the test surface TS is one, k is omitted in equation (5).Note that D₁=Λ₁₂/{2k·ng(λ₁,λ₂)}·(M+{(φ₂−φ₁)/2π}) in fact.

On the other hand, the absolute distance D can also be expressed usingthe second reference wavelength λ₂ by

$\begin{matrix}{D = {\frac{\lambda_{2}}{2\;{n\left( \lambda_{2} \right)}}\left( {N_{12} + \frac{\phi_{2}}{2\;\pi}} \right)}} & (6)\end{matrix}$Since the second reference wavelength λ₂ is shorter than the syntheticwavelength Λ₁₂, the absolute distance D can accurately be obtained.

Using equation (5), the order N₁₂ of interference can be obtained by

$\begin{matrix}\begin{matrix}{N_{12} = {{round}\left( {\frac{2\;{n\left( \lambda_{2} \right)}D_{1}}{\lambda_{2}} - \frac{\phi_{2}}{2\;\pi}} \right)}} \\{= {{round}\;\left( {{\left( {M + \frac{\phi_{2} - \phi_{1}}{2\;\pi}} \right)\frac{{n\left( \lambda_{2} \right)}\Lambda_{12}}{{n_{g}\left( {\lambda_{1},\lambda_{2}} \right)}\lambda_{2}}} - \frac{\phi_{2}}{2\;\pi}} \right)}}\end{matrix} & (7)\end{matrix}$where round( ) is the function for rounding an argument to an integer.Equation (7) includes a term representing the ratio of the refractiveindex to the group index, which is of an order of about 1+10⁻⁶, and cantherefore be approximated to 1. However, if the ratio of the refractiveindex to the group index is not negligible (for example, the ratio ofthe synthetic wavelength Λ₁₂ to the second reference wavelength λ₂ ishigh), the environment in the space between the reference surface RS andthe test surface TS is detected (S216) when detecting the phases insteps S206 and S212. This allows calculation of the ratio of therefractive index to the group index.

To determine (calculate) the order N₁₂ of interference without anyerror, the error of the argument of round( ) in equation (7) need onlybe smaller than ½. Let dφ be the phase detection error, dλ₂ be the error(error from the designed value) of the second reference wavelength λ₂,and dΛ₂ be the error (error from the designed value) of syntheticwavelength Λ₁₂. When M>>1, and Λ₁₂/λ₂, it is necessary to only satisfy

$\begin{matrix}{{{\sqrt{2}\frac{d\;\phi}{2\;\pi}\frac{\Lambda_{12}}{\lambda_{2}}} + {\frac{2\; D}{\lambda_{2}}\frac{d\;\Lambda_{12}}{\Lambda_{12}}} + {\frac{2\; D}{\lambda_{2}}\frac{d\;\lambda_{2}}{\lambda_{2}}}} < \frac{1}{2}} & (8)\end{matrix}$

In inequality (8), when the absolute distance D is 1.5 m, and the secondreference wavelength λ₂ is 1.5 μm, D/λ₂ is 10⁶. On the other hand,dΛ₁₂/Λ₁₂ and dλ₂/λ₂ can implement 10⁻⁷ by using the Fabry-Perot etalon108. Hence, the first term on the left-hand side is the constraint ofequation (7). However, inequality (8) needs to hold for all absolutedistances D, that is, a range Dmax of absolute distances measurable bythe measuring apparatus 1.

The heterodyne method adopted by the measuring apparatus 1 of thisembodiment can accurately detect a phase. Hence, a detection accuracy ofabout 10⁻⁴ [wave] can easily be obtained. If accurate phase detectioncan be implemented, the synthetic wavelength Λ₁₂ can be extended to 10³times the second reference wavelength λ₂. When the second referencewavelength λ₂ is 1.5 μm, the synthetic wavelength Λ₁₂ can be extended upto 1.5 mm. Hence, the wavelength difference (wavelength change amount)between the first reference wavelength λ₁ and the second referencewavelength λ₂ is 1.5 nm. If the wavelength difference is as small asabout 1.5 nm, wavelength change (wavelength scanning) can be done evenusing a DFB-DL. Hence, the measuring apparatus 1 can be implemented by asimple arrangement without using any complex light source such as anexternal cavity semiconductor laser.

In step S216, the environment in the space near the test surface TS,that is, between the reference surface RS and the test surface TS isdetected. In this embodiment, the humidity in the space between thereference surface RS and the test surface TS is assumed to beguaranteed. The environment detection unit 122 detects a temperature t[° C.] and atmospheric pressure p [Pa] in the space, and inputs thedetection result to the processing unit 124.

In step S218, the phase φ₂ at the second reference wavelength λ₂ isdetected, as in step S212. The phase φ₂ corresponding to the opticalpath difference between the reference surface RS (reference light) andthe test surface TS (test light) is thus obtained.

In step S220, the refractive index (atmospheric refractive index) in thespace between the reference surface RS and the test surface TS iscalculated, and the absolute distance D between the reference surface RSand the test surface TS is obtained. First, using the Edlen's formulabased on the temperature t [° C.] and atmospheric pressure p [Pa], arefractive index (atmospheric refractive index) n of dry air iscalculated by

$\begin{matrix}\left\{ \begin{matrix}{{n(\lambda)} = {1 + {\frac{p \cdot 10^{- 8}}{96095.43}\left\lbrack {8342.54 + \frac{2406147}{130 - {S(\lambda)}} + \frac{15998}{38.9 - {S(\lambda)}}} \right\rbrack}}} \\\left\lbrack \frac{1 + {10^{- 8}\left( {0.601 - {0.00972\; t}} \right)p}}{1 + {0.003661\; t}} \right\rbrack \\{{S(\lambda)} = {1/\left( {\lambda_{2} \cdot 10^{6}} \right)^{2}}}\end{matrix} \right. & (9)\end{matrix}$

Note that the gas in the space between the reference surface RS and thetest surface TS may be not a dry gas. In this case, the environmentdetection unit 122 needs to include a hygrometer for detecting thehumidity of the gas. An Edlen's formula including a humidity correctionterm is used in place of equation (9).

Using the order N₁₂ of interference calculated in step S214, the phaseφ₂ detected in step S218, and the refractive index n(λ₂), the absolutedistance D can be obtained by equation (6). Especially when the absolutedistance D is to be obtained first after executing theorder-of-interference determination processing, the absolute distance D(absolute distance D₂) is obtained by

$\begin{matrix}{D = {\frac{\lambda_{2}}{2\;{n\left( \lambda_{2} \right)}}\left( {{{round}\left( {\frac{2\;{n\left( \lambda_{2} \right)}D_{1}}{\lambda_{2}} - \frac{\phi_{2}}{2\;\pi}} \right)} + \frac{\phi_{2}}{2\;\pi}} \right)}} & (10)\end{matrix}$(see equations (5), (6), and (7)).

In step S222, it is determined whether or not to end the measurementprocessing (the processing of obtaining the absolute distance betweenthe reference surface RS and the test surface TS). Upon determining toend the measurement processing, the measurement processing ends. If itis determined not to end the measurement processing, the process returnsto step S202 to determine whether or not to executeorder-of-interference determination processing. If it is determined notto execute order-of-interference determination processing, steps S216 toS220 are repeatedly executed. A change of the order of interferencecaused by movement of the test surface TS is corrected using a phasedetection history. More specifically, letting φ₂(i) be the result of ithphase detection, and φ₂(i−1) be the result of (i−1)th phase detection,an order N₁₂(i) of interference in obtaining the ith absolute distanceis given by

$\begin{matrix}{{N_{12}(i)} = {{N_{12}\left( {i - 1} \right)} + {{round}\left( \frac{{\phi_{2}\left( {i - 1} \right)} - {\phi_{2}(i)}}{2\;\pi} \right)}}} & (11)\end{matrix}$

As described above, according to the measuring apparatus 1 of thisembodiment, it is possible to accurately measure the absolute distancebetween the reference surface RS and the test surface TS using a simplearrangement.

<Second Embodiment>

FIG. 4 is a schematic view showing the arrangement of a measuringapparatus 1A according to the second embodiment of the presentinvention. The measuring apparatus 1A basically has the same arrangementas that of the measuring apparatus 1. However, the measuring apparatus1A includes, as an environment detection unit 122A for detecting therefractive index of a gas near a test surface TS, a light source 132 anda phase detection unit 134 b which detects the optical path differencebetween a reference surface RS and the test surface TS using lightemitted by the light source 132. The measuring apparatus 1A alsoincludes a phase detection unit 134 a, spectral elements 136 a and 136b, and light amount detection units 138 a and 138 b.

The measuring apparatus 1A can detect the integrated value of refractiveindices (atmospheric refractive indices) near the test surface TS by thetwo-color method. For this reason, even when the temperaturedistribution is large in the direction of measurement optical path, theeffective refractive index (atmospheric refractive index) can accuratelybe obtained. Additionally, not a heterodyne scheme but a homodyne schemeis employed as the phase detection scheme, thereby implementing a moresimple arrangement.

Light emitted by a light source 102 is split (branched) by a beamsplitter 104 a. Light emitted by the light source 132 serving as a thirdlight source also enters the beam splitter 104 a so as to have a rayaxis coaxial with that of the light from the light source 102 (sameoptical path). The light is split by the beam splitter 104 a. The lightsource 132 emits light having a wavelength different from that of thelight from the light source 102. In this embodiment, a DFB-DL is used asthe light source 132, like the light source 102.

One of the two light components split by the beam splitter 104 a passesthrough a Fabry-Perot etalon 108, and is split by the spectral element136 a into the light from the light source 102 and that from the lightsource 132. As for the amount of light transmitted through theFabry-Perot etalon 108, the light amount detection unit 138 a detectsthe amount of the light from the light source 102, and the light amountdetection unit 138 b detects the amount of the light from the lightsource 132.

The light amounts detected by the light amount detection units 138 a and138 b are input to a light source control unit 112. The light sourcecontrol unit 112 independently controls the light sources 102 and 132 sothat the wavelength of light emitted by the light source 102 and thewavelength of light emitted by the light source 132 stabilize withrespect to different frequency components (reference wavelengths) of thetransmission spectrum of the Fabry-Perot etalon 108. Note that in thisembodiment, independent light sources are used as the light sources 102and 132. However, the light source 102 may emit a double wave withoutusing the light source 132. In this case, the wavelength of light to beemitted by the light source 132 need not be controlled. The double wavecan easily be generated using a waveguide PPLN as a wavelengthconversion element.

The other of the two light components split by the beam splitter 104 aenters a polarizing beam splitter 118. The light reflected by thepolarizing beam splitter 118 is reflected by the reference surface RS.The light is reflected by the polarizing beam splitter 118 again, andenters the spectral element 136 b as reference light. The lighttransmitted through the polarizing beam splitter 118 is reflected by thetest surface TS. The light passes through the polarizing beam splitter118 again, and enters the spectral element 136 b as test light.

The spectral element 136 b is formed from, for example, a dichroicmirror to separate the light from the light source 102 and that from thelight source 132 which are incident coaxially. However, the spectralelement 136 b is not limited to the dichroic mirror. A prism, bulk typediffraction grating, or array waveguide type diffraction grating is alsousable, and the device can selected from the viewpoint of necessarywavelength resolution and cost.

The light from the light source 102 passes through the spectral element136 b, and enters the phase detection unit 134 a. The phase detectionunit 134 a detects a phase (interference phase) corresponding to theoptical path difference between the reference surface RS (referencelight) and the test surface TS (test light) at the wavelength of lightfrom the light source 102. On the other hand, the light from the lightsource 132 is reflected by the spectral element 136 b, and enters thephase detection unit 134 b. The phase detection unit 134 b detects aphase (interference phase) corresponding to the optical path differencebetween the reference surface RS (reference light) and the test surfaceTS (test light) at the wavelength of light from the light source 132.

In this embodiment as well, the polarizing beam splitter 118 is used asa beam splitting element of the measuring apparatus 1A. This allowslight reflected by each of the reference surface and the test surface tobe split in accordance with the polarization direction. It is thereforepossible to perform homodyne detection by phase difference control usingthe difference in polarization direction, and thus implement accuratephase detection.

FIG. 5 is a view showing the detailed arrangement of the phase detectionunits 134 a and 134 b. Each of the phase detection units 134 a and 134 bincludes a λ/4 plate 502 having a fast axis of 45° with respect to theangle of polarization axes of the test light and reference light, agrating beam splitter 504, a polarizer array 506, and a plurality oflight amount detectors 508 a, 508 b, and 508 c. The λ/4 plate 502 has afunction of a phase difference adding unit which adds a plurality ofknown phase differences to incident light. In this embodiment, the λ/4plate 502 converts the test light and reference light into right-handedcircularly polarized light and left-handed circularly polarized light,respectively. The light transmitted through the λ/4 plate 502 is splitinto three light components, that is, 0th-order diffraction componentand ±1st-order diffraction components in the same light amount by thegrating beam splitter 504. The three light components pass through thepolarizer array 506 which is arranged such that the light componentspass in different polarization directions (polarizer angles), and aredetected by the light amount detectors 508 a, 508 b, and 508 c.

When the angle of each polarizer of the polarizer array 506 is set at a120° pitch, light amounts Ia, Ib, and Ic detected by the light amountdetectors 508 a, 508 b, and 508 c, respectively, are given byI _(a) =I ₀{1+V cos(φ)}I _(b) =I ₀{1+V cos(φ+2π/3)}  (12)I _(c) =I ₀{1+V cos(φ+4π/3)}where φ is the phase of the interference signal generated by the opticalpath difference between the reference surface RS (reference light) andthe test surface TS (test light). Referring to equations (12), the phaseφ can be obtained by

$\begin{matrix}{\phi = {\tan^{- 1}\left( \frac{{- \sqrt{3}}\left( {I_{b} - I_{c}} \right)}{{2\; I_{a}} - I_{b} - I_{c}} \right)}} & (13)\end{matrix}$

The processing unit 124 obtains the phases from the detection results ofthe phase detection units 134 a and 134 b. More specifically, usingequation (13), the processing unit 124 obtains the phase correspondingto the optical path difference between the reference surface RS and thetest surface TS at the wavelength of light from the light source 102 andthe phase corresponding to the optical path difference between thereference surface RS and the test surface TS at the wavelength of lightfrom the light source 132.

In this embodiment, each of the phase detection units 134 a and 134 bdetects the intensity of the interference signal for three known phasedifferences, as described above. Instead, the intensity of theinterference signal for a plurality of known phase differences may bedetected. The phase differences may spatially be added by generatingtilt fringes between reference light and test light using a prism havingbirefringence. Note that the number of known phase differences or theinterval between the known phase differences can be selected as neededin accordance with the necessary accuracy.

Note that since no high-frequency signals exist in homodyne detection,the detection system can be constituted less expensively than inheterodyne detection. As for the phase detection accuracy, an accuracyof about 10⁻⁴ [wave] can be implemented as in heterodyne detection bycorrecting the gains, offsets, and phase characteristics of the lightamount detectors 508 a, 508 b, and 508 c.

Measurement processing (that is, processing of causing the processingunit 124 to obtain the absolute distance between the reference surfaceRS and the test surface TS) of the measuring apparatus 1A will bedescribed with reference to FIG. 6. Note that steps S602 to S614 of FIG.6 are the same as steps S202 to S214 of FIG. 2, and a detaileddescription thereof will not be repeated here. An order N₁₂ ofinterference is assumed to be calculated (determined) in step S614.

In step S616, a phase φ₂ at a second reference wavelength λ₂ and a phaseφ₂₂ at a wavelength λ₂₂ of light from the light source 132 are detected.

In step S618, an absolute distance D between the reference surface RSand the test surface TS is obtained. In this embodiment, the absolutedistance D is obtained by correcting the refractive index of the gas inthe space between the reference surface RS and the test surface TS usingthe dispersion of air at the two wavelengths. An optical path differenceOPD(λ₂) at the second reference wavelength λ₂ and an optical pathdifference OPD(λ₂₂) at the wavelength λ₂₂ are given by

$\begin{matrix}\left\{ \begin{matrix}{{O\; P\;{D\left( \lambda_{2} \right)}} = {{2\;{n\left( \lambda_{2} \right)}D} = {\lambda_{2}\left( {N_{12} + \frac{\phi_{2}}{2\;\pi}} \right)}}} \\{{O\; P\;{D\left( \lambda_{22} \right)}} = {{2\;{n\left( \lambda_{22} \right)}D} = {\lambda_{22}\left( {N_{22} + \frac{\phi_{22}}{2\;\pi}} \right)}}}\end{matrix} \right. & (14)\end{matrix}$where N₂₂ is the order of interference at the wavelength λ₂₂.

A given by

$\begin{matrix}{A = \frac{{n\left( \lambda_{2} \right)} - 1}{{n\left( \lambda_{2} \right)} - {n\left( \lambda_{22} \right)}}} & (15)\end{matrix}$is called an A coefficient which is known to be constant independentlyof a variation in the temperature or atmospheric pressure of the drygas. Hence, the A coefficient for the second reference wavelength λ₂ andthe wavelength λ₂₂ can be obtained in advance.

From equations (14) and (15), we obtain

$\begin{matrix}\left\{ \begin{matrix}{\begin{matrix}{D = {{{OPD}\left( \lambda_{2} \right)} - {A \cdot \left( {{{OPD}\left( \lambda_{2} \right)} - {{OPD}\left( \lambda_{22} \right)}} \right)}}} \\{= {{\lambda_{2}\left( {N_{12} + \frac{\phi_{2}}{2\pi}} \right)} - {A \cdot \left\lbrack {{\lambda_{2}\left( {N_{12} + \frac{\phi_{2}}{2\pi}} \right)} - {\lambda_{22}\left( {N_{22} + \frac{\phi_{22}}{2\pi}} \right)}} \right\rbrack}}}\end{matrix}} \\{N_{22} = {{round}\left( {{\frac{n\left( \lambda_{22} \right)}{n\left( \lambda_{2} \right)}\frac{{OPD}\left( \lambda_{2} \right)}{\lambda_{22}}} - \frac{\phi_{22}}{2\pi}} \right)}}\end{matrix} \right. & (16)\end{matrix}$The absolute distance D can be obtained by equations (16) using theorder N₁₂ of interference calculated in step S614, the phases φ₂ and φ₂₂detected in step S616, and the A coefficient obtained in advance.

Referring to equations (16), to calculate the order N₂₂ of interference,the ratio of a refractive index n(λ₂) at the second reference wavelengthλ₂ to a refractive index n(λ₂₂) at the wavelength λ₂₂ is necessary.However, the ratio is of an order of about 1+10⁻⁵ under generalconditions, and can therefore be approximated to 1. If the approximationis impossible, the wavelength of light to be emitted by the light source132 is changed (scanned) to calculate (determine) the order N₂₂ ofinterference, as in steps S604 to S614.

If the gas in the space between the reference surface RS and the testsurface TS is not a dry gas, the humidity in the space between thereference surface RS and the test surface TS is detected, and the Acoefficient is updated in accordance with the humidity change, therebyobtaining the absolute distance D. Note that to detect the humidity inthe space between the reference surface RS and the test surface TS, ahygrometer and a thermometer need to be arranged near the test surfaceTS.

In step S620, it is determined whether or not to end the measurementprocessing (the processing of obtaining the absolute distance betweenthe reference surface RS and the test surface TS). Upon determining toend the measurement processing, the measurement processing ends. If itis determined not to end the measurement processing, the process returnsto step S602 to determine whether or not to executeorder-of-interference determination processing.

As described above, according to the measuring apparatus 1A of thisembodiment, it is possible to accurately measure the absolute distancebetween the reference surface RS and the test surface TS using a simplearrangement while guaranteeing the variation in the refractive index ofthe gas in the space between the reference surface RS and the testsurface TS.

<Third Embodiment>

FIG. 7 is a schematic view showing the arrangement of a measuringapparatus 1B according to the third embodiment of the present invention.The measuring apparatus 1B basically has the same arrangement as that ofthe measuring apparatus 1 or 1A. However, the measuring apparatus 1Bincludes an interferometer 140 as an environment detection unit fordetecting the refractive index of a gas near a test surface TS. Theinterferometer 140 detects an interference signal corresponding to theoptical path difference between the vacuum reference optical path (firstoptical path) of a vacuum atmosphere having a known length and theatmospheric reference optical path (second optical path) of anatmosphere having the same length as that of the vacuum referenceoptical path. The measuring apparatus 1B also includes phase detectionunits 152 a and 152 b.

The measuring apparatus 1B can detect a refractive index using theinterferometer 140 serving as an environment detection unit fordetecting the refractive index (atmospheric refractive index) of the gasnear the test surface TS without assuming a refractive index dispersionformula or the like. As for the influence of an error of theinterferometer length, the interferometer for measuring the optical pathdifference between the vacuum reference optical path and the atmosphericreference optical path is constituted to reduce the error sensitivityand implement accurate refractive index detection.

Light emitted by a light source 102 is split (branched) by a beamsplitter 104 a. Out of the two light components split by the beamsplitter 104 a, a light component reflected by the beam splitter 104 apasses through a Fabry-Perot etalon 108, and enters an intensitydetection unit 110. Based on the etalon transmission intensity detectedby the intensity detection unit 110, a light source control unit 112controls the wavelength of light to be emitted by the light source 102(that is, stabilizes the wavelength with respect to a transmissionspectrum of the Fabry-Perot etalon 108).

A light component transmitted through the beam splitter 104 a is splitby a non-polarizing beam splitter 114. Out of the two light componentssplit by the non-polarizing beam splitter 114, a light componenttransmitted through the non-polarizing beam splitter 114 enters apolarizing beam splitter 118. The light reflected by the polarizing beamsplitter 118 is reflected by a reference surface RS. The light isreflected by the polarizing beam splitter 118 again, and enters thephase detection unit 152 a as reference light. The light transmittedthrough the polarizing beam splitter 118 is reflected by the testsurface TS. The light passes through the polarizing beam splitter 118again, and enters the phase detection unit 152 a as test light. Thephase detection unit 152 a has the same arrangement as that of the phasedetection units 134 a and 134 b of the second embodiment, and detects aphase corresponding to the optical path difference between the referencesurface RS (reference light) and the test surface TS (test light).

Out of the two light components split by the non-polarizing beamsplitter 114, a light component reflected by the non-polarizing beamsplitter 114 enters the interferometer 140. In the interferometer 140,an optical path difference is generated between a vacuum referenceoptical path through a vacuum medium between a first reference surface146 and a second reference surface 147 and an atmospheric referenceoptical path through an atmospheric medium. Note that a phasecorresponding to the optical path difference between the vacuumreference optical path and the atmospheric reference optical path isdetected by the phase detection unit 152 b.

The arrangement of the interferometer 140 will be described here. Lightthat enters the interferometer 140 is split by a beam displacer 141 inaccordance with the polarization direction. Light that travels straightthrough the beam displacer 141 will be referred to as atmosphericreference light, and light horizontally displaced by the wake-off of thebeam displacer 141 will be referred to as vacuum reference lighthereinafter. The beam displacer 141 is formed from, for example, auniaxial crystal such as YVO4. The beam displacer 141 may be formed byarranging a plurality of polarizing beam splitters.

The polarization direction of vacuum reference light transmitted throughthe beam displacer 141 is converted into the same polarization directionas that of the atmospheric reference light by a λ/2 plate 142. Then, thevacuum reference light enters a polarizing beam splitter 143. On theother hand, atmospheric reference light transmitted through the beamdisplacer 141 enters the polarizing beam splitter 143 withoutintervening the λ/2 plate 142. The vacuum reference light andatmospheric reference light pass through the polarizing beam splitter143, are converted into circularly polarized light by a λ/4 plate 145,and pass through the first reference surface 146. A vacuum cell 148 isfixed between the first reference surface 146 and the second referencesurface 147. The vacuum reference light propagates inside the vacuumcell 148. The atmospheric reference light propagates in the atmosphere.The vacuum reference light and atmospheric reference light are reflectedby the second reference surface 147. After the polarization directionsare converted by the λ/4 plate 145 into those perpendicular to thepolarization directions in the forward path, the light components enterthe polarizing beam splitter 143. The vacuum reference light andatmospheric reference light are reflected by the polarizing beamsplitter 143, and enter a corner cube 144. The vacuum reference lightand atmospheric reference light reflected by the corner cube 144 arereflected by the polarizing beam splitter 143 again so as toreciprocally travel between the polarizing beam splitter 143 and thesecond reference surface 147. The vacuum reference light and atmosphericreference light reciprocally traveled between the polarizing beamsplitter 143 and the second reference surface 147 pass through thepolarizing beam splitter 143. Only the atmospheric reference lightenters the beam displacer 141 after its polarization direction isconverted into a perpendicular direction by the λ/2 plate 142. In thebeam displacer 141, wake-off occurs only in the atmospheric referencelight. Hence, the vacuum reference light and atmospheric reference lightare converted into coaxial light through the beam displacer 141, andenter the phase detection unit 152 b. The vacuum reference light andatmospheric reference light have a common optical path length except forthe optical path between the first reference surface 146 and the secondreference surface 147. For this reason, the phase detection unit 152 bdetects an optical path difference corresponding to the mediumdifference (vacuum and atmosphere) between the first reference surface146 and the second reference surface 147.

Measurement processing (that is, processing of causing the processingunit 124 to obtain the absolute distance between the reference surfaceRS and the test surface TS) of the measuring apparatus 1B will bedescribed with reference to FIG. 8. Note that steps S802, S804, and S810of FIG. 8 are the same as steps S202, S204, and S210 of FIG. 2, and adetailed description thereof will not be repeated here. In thisembodiment, however, even when the phase detection history of theinterferometer 140 is lost, order-of-interference determinationprocessing needs to be executed. In steps S804 to S814, calculation ofan order N₁₂ of interference is the same as in the first embodiment, andcalculation of an order N^(ri) ₁₂ of interference of the interferometer140 is added.

In step S806, a phase φ₁ at a first reference wavelength λ₁ and a phaseφ^(ri) ₁ of the interferometer 140 are detected. Similarly, in stepS812, a phase φ₂ at a second reference wavelength λ₂ and a phase φ^(ri)₂ of the interferometer 140 are detected. Letting D^(ri) be thegeometrical distance between the first reference surface 146 and thesecond reference surface 147, the phases φ^(ri) ₁ and φ^(ri) ₂ are givenby

$\begin{matrix}\left\{ \begin{matrix}{\phi_{1}^{ri} = {2\pi\;{{mod}\left( {\frac{4\left( {{n\left( \lambda_{1} \right)} - 1} \right)D^{ri}}{\lambda_{1}},1} \right)}}} \\{\phi_{2}^{ri} = {2\pi\;{{mod}\left( {\frac{4\left( {{n\left( \lambda_{2} \right)} - 1} \right)D^{ri}}{\lambda_{2}},1} \right)}}}\end{matrix} \right. & (17)\end{matrix}$

In step S808, an order M^(ri) of interference of a synthetic wavelengthΛ₁₂ is calculated while continuously changing (scanning) the wavelengthof light to be emitted by the light source 102 from the first referencewavelength λ₁ to the second reference wavelength λ₂. The order M^(ri) ofinterference is given by

$\begin{matrix}{M^{ri} = {\frac{4\left( {{n_{g}{n_{g}\left( {\lambda_{1},\lambda_{2}} \right)}} - 1} \right)D^{ri}}{\Lambda_{12}} - \left( {\phi_{2}^{ri} - \phi_{1}^{ri}} \right)}} & (18)\end{matrix}$

In step S814, the orders N₁₂ and N^(ri) ₁₂ of interference at the secondreference wavelength λ₂ are calculated. Based on equations (17) and(18), the order N^(ri) ₁₂ of interference is given by

$\begin{matrix}\begin{matrix}{N_{12}^{ri} \equiv {{round}\mspace{11mu}\left( {\frac{4\left( {{n\left( \lambda_{2} \right)} - 1} \right)D^{ri}}{\lambda_{2}} - \frac{\phi_{2}^{ri}}{2\pi}} \right)}} \\{= {{round}\mspace{11mu}\left( {{\left( {M^{ri} + \frac{\phi_{2}^{ri} - \phi_{1}^{ri}}{2\pi}} \right)\frac{{n\left( \lambda_{2} \right)}\Lambda}{{n_{g}\left( {\lambda_{1},\lambda_{2}} \right)}\lambda_{2}}} - \frac{\phi_{2}^{ri}}{2\pi}} \right)}}\end{matrix} & (19)\end{matrix}$Calculating the order N^(ri) ₁₂ of interference allows the optical pathdifference between the vacuum reference light to be determined and theatmospheric reference light without ambiguity of 2π. Note thatcalculation of the order N₁₂ of interference is the same as in the firstembodiment, and a detailed description thereof will not be repeatedhere.

In step S816, the phase φ₂ at the second reference wavelength λ₂ and thephase φ^(ri) ₂ of the interferometer 140 are detected.

In step S818, the refractive index (atmospheric refractive index) in thespace between the reference surface RS and the test surface TS iscalculated, thereby obtaining the absolute distance D between thereference surface RS and the test surface TS. Using the order N^(ri) ₁₂of interference calculated in step S814 and the phase φ^(ri) ₂ detectedin step S816, the refractive index n in the space between the referencesurface RS and the test surface TS is calculated by

$\begin{matrix}{{n\left( \lambda_{2} \right)} = {{\left( {N_{12}^{ri} + \frac{\phi_{2}^{ri}}{2\pi}} \right)\frac{\lambda_{2}}{4D^{ri}}} + 1}} & (20)\end{matrix}$

The geometrical distance D^(ri) between the first reference surface 146and the second reference surface 147 is assumed to be known. The firstterm on the right-hand side of equation (20) is the difference of theatmospheric refractive index from the vacuum refractive index, and istherefore about 3×10⁻⁴ in general. Hence, the error of the atmosphericrefractive index generated by an error ΔD^(ri) of the distance D^(ri) isof an order of 3×10⁻⁴×ΔD_(ri)/D^(ri). This is more advantageous for theerror of the same distance by only 3×10⁻⁴ in terms of accuracy becausethe order of a reference interferometer including no vacuum referenceoptical path is ΔD_(ri)/D^(ri).

The absolute distance D can be obtained by equation (6) described aboveusing the order N₁₂ of interference calculated in step S814, the phaseφ₂ detected in step S816, and equation (20).

In step S820, it is determined whether or not to end the measurementprocessing (the processing of obtaining the absolute distance betweenthe reference surface RS and the test surface TS). Upon determining toend the measurement processing, the measurement processing ends. If itis determined not to end the measurement processing, the process returnsto step S802 to determine whether or not to executeorder-of-interference determination processing.

As described above, the measuring apparatus 1B of this embodiment has anarrangement with less influence of the distance error of the referenceinterferometer, and guarantees the variation in the refractive index ofthe gas in the space between the reference surface RS and the testsurface TS. Hence, according to the measuring apparatus 1B of thisembodiment, it is possible to accurately measure the absolute distancebetween the reference surface RS and the test surface TS using a simplearrangement.

<Fourth Embodiment>

FIG. 9 is a schematic view showing the arrangement of a measuringapparatus 1C according to the fourth embodiment of the presentinvention. The measuring apparatus 1C basically has the same arrangementas that of the measuring apparatus 1, 1A, or 1B. However, the measuringapparatus 1C includes a light source 162, gas cell 164, light amountdetection units 166 a, 166 b, and 166 c, spectral elements 168 a and 168b, and phase detection units 172 a and 172 b.

In the measuring apparatus 1C, the change amount of the wavelength oflight from a light source 102 and the accuracy of wavelength change arereduced by using the synthetic wavelength of the wavelength of lightemitted by the light source 102 and the wavelength of light emitted bythe light source 162. In addition, when a plurality of interferometersare formed for a light source, stable measurement can always beperformed using the light source 162. Hence, when changing thewavelength for determining the order of interference of an arbitrarymeasurement axis, an arrangement without any influence of wavelengthchange can be implemented for an interference axis (interferometer)which requires no order-of-interference determination.

Each of light emitted by the light source 102 and light emitted by thelight source 162 is split (branched) by a beam splitter 104 a. One lightenters a Fabry-Perot etalon 108. The other light enters a polarizingbeam splitter 118. The light emitted by the light source 162 serving asa second light source is also split by a beam splitter 104 b, and entersthe gas cell 164.

Note that in this embodiment, independent light sources are used as thelight sources 102 and 162. However, the light sources may be formed byintegrating a plurality of semiconductor lasers into one element, like amulti-wavelength light source used in optical communication. This isadvantageous in terms of cost and apparatus dimensions.

The light amount detection unit 166 a detects the amount of the lighttransmitted through the gas cell 164 (light from the light source 162).In this embodiment, as the wavelength of light emitted by the lightsource 102, a wavelength near 1.5 μm is used. As the filler gas of thegas cell 164, acetylene is used. However, the filler gas of the gas cell164 is not limited to acetylene. It can be any other filler gas such ascarbon monoxide or hydrogen cyanide usable in the wavelength band near1.5 μm. One of the filler gases is selected as needed because they havedifferent wavelength bands and center wavelength accuracies.

On the other hand, the light transmitted through the Fabry-Perot etalon108 is split by the spectral element 168 a into the light from the lightsource 102 and the light from the light source 162. As for the amount oflight transmitted through the Fabry-Perot etalon 108, the light amountdetection unit 166 b detects the amount of the light from the lightsource 102, and the light amount detection unit 166 c detects the amountof the light from the light source 162.

FIGS. 10A to 10C show the transmission spectrum of the gas cell 164, thetransmission spectrum of the Fabry-Perot etalon 108, and the spectrum oflight emitted by each of the light sources 102 and 162. Based on thelight amount detected by the light amount detection unit 166 a, a lightsource control unit 112 controls the light source 162 so that thewavelength of light to be emitted by the light source 162 stabilizes toa third reference wavelength λ₃ corresponding to the absorption line ofthe gas cell 164. Additionally, based on the light amount detected bythe light amount detection unit 166 c, the light source control unit 112controls the optical path length of the Fabry-Perot etalon 108 so thatthe transmission spectrum of the Fabry-Perot etalon 108 matches thethird reference wavelength λ₃. Note that the internal medium of theFabry-Perot etalon 108 is vacuum, and the optical path length iscontrolled using the temperature of the etalon. Furthermore, based onthe light amount detected by the light amount detection unit 166 b, thelight source control unit 112 controls the light source 102 so that thewavelength of light to be emitted by the light source 102 stabilizes tothe transmission spectrum of the Fabry-Perot etalon 108. That is, thewavelength of light emitted by the light source 102 can stabilize to afirst reference wavelength λ₁ or second reference wavelength λ₂, and canbe changed (scanned) between the first reference wavelength λ₁ and thesecond reference wavelength λ₂.

In this embodiment, the Fabry-Perot etalon 108 is used in addition tothe gas cell 164, thereby improving the accuracy of the referencewavelength. However, when the conditions to determine the order ofinterference to be described later are satisfied, the Fabry-Perot etalon108 need not be used.

The light that enters the polarizing beam splitter 118 generates aninterference signal corresponding to the optical path difference betweena reference surface RS and a test surface TS at the wavelength of lightfrom each light source (light source 102 or 162). The phase detectionunit 172 a detest a phase (interference phase) corresponding to theoptical path difference between the reference surface RS and the testsurface TS at the first reference wavelength λ₁ via the spectral element168 b. The phase detection unit 172 b detest a phase (interferencephase) corresponding to the optical path difference between thereference surface RS and the test surface TS at the third referencewavelength λ₃ via the spectral element 168 b.

In this embodiment, the phase detection unit 172 a for the light fromthe light source 102 and the phase detection unit 172 b for the lightfrom the light source 162 are independently formed, therebysimultaneously detecting the phase at the first reference wavelength λ₁and that at the third reference wavelength λ₃. However, the lightsources 102 and 162 may be switched using one phase detection unit. Inthis case, the measuring apparatus 1C can have a more simplearrangement.

Measurement processing (that is, processing of causing a processing unit124 to obtain the absolute distance between the reference surface RS andthe test surface TS) of the measuring apparatus 1C will be describedwith reference to FIG. 11. Note that steps S1102 to S1112 of FIG. 11 arethe same as steps S202 to S212 of FIG. 2, and a detailed descriptionthereof will not be repeated here.

In step S1114, a phase φ₃ at the third reference wavelength λ₃ isdetected. The phase φ₃ at the third reference wavelength λ₃ is given by

$\begin{matrix}{\phi_{3} = {2{\pi \cdot {{mod}\left( {\frac{2{n\left( \lambda_{3} \right)}D}{\lambda_{3}},1} \right)}}}} & (21)\end{matrix}$

In step S1116, an order N₃ of interference at the third referencewavelength λ₃ is calculated. Let Λ₁₃ be the synthetic wavelength of thefirst reference wavelength λ₁ and the third reference wavelength λ₃represented by λ₁·λ₃/|λ₁−λ₃|. In this case, the absolute distance Dbetween the reference surface RS and the test surface TS, the thirdreference wavelength λ₃, and the synthetic wavelength Λ₁₃ have relationsrepresented by

$\begin{matrix}{{D = {\frac{\lambda_{3}}{2{n\left( \lambda_{3} \right)}}\left( {N_{3} + \frac{\phi_{3}}{2\pi}} \right)}}{and}} & (22) \\{D = {\frac{\Lambda_{13}}{2{n_{g}\left( {\lambda_{1},\lambda_{2}} \right)}}\left( {M_{13} + \frac{\phi_{3} - \phi_{1}}{2\pi}} \right)}} & (23)\end{matrix}$

In equations (5), (22), and (23), the wavelength and the syntheticwavelengths have a relation λ₃<<Λ₁₃<<Λ₁₂. Hence, the orders N₃ and M₁₃of interference are given by

$\begin{matrix}\left\{ \begin{matrix}{N_{3} = {{round}\mspace{11mu}\left( {{\left( {M_{13} + \frac{\phi_{3} - \phi_{1}}{2\pi}} \right)\frac{{n\left( \lambda_{3} \right)}\Lambda_{13}}{{n_{g}\left( {\lambda_{1},\lambda_{3}} \right)}\lambda_{3}}} - \frac{\phi_{3}}{2\pi}} \right)}} \\{M_{13} = {{round}\mspace{11mu}\left( {{\left( {M + \frac{\phi_{2} - \phi_{1}}{2\pi}} \right)\frac{{n_{g}\left( {\lambda_{1},\lambda_{3}} \right)}\Lambda_{\;}}{{n_{g}\left( {\lambda_{1},\lambda_{2}} \right)}\Lambda_{13}}} - \frac{\phi_{3} - \phi_{1}}{2\pi}} \right)}}\end{matrix} \right. & (24)\end{matrix}$

Let dφ be the phase detection error. Conditions to determine (calculate)the orders N₃ and M₁₃ of interference without any error are representedby

$\begin{matrix}{{{\sqrt{2}\frac{d\;\phi}{2\pi}\frac{\Lambda_{13}}{\lambda_{3}}} + {\frac{2D}{\lambda_{3}}\frac{d\;\Lambda_{13}}{\Lambda_{13}}} + {\frac{2D}{\lambda_{3}}\frac{d\;\lambda_{3}}{\lambda_{3}}}} < \frac{1}{2}} & (25) \\{{{\sqrt{2}\frac{d\;\phi}{2\pi}\frac{\Lambda}{\Lambda_{13}}} + {\frac{2D}{\Lambda_{13}}\frac{d\;\Lambda_{12}}{\Lambda_{12}}} + {\frac{2D}{\Lambda_{13}}\frac{d\;\Lambda_{13}}{\Lambda_{13}}}} < \frac{1}{2}} & (26)\end{matrix}$

In inequality (25), when the absolute distance D is 1.5 m, and the thirdreference wavelength λ₃ is 1.5 μm, D/λ₃ is 10⁶. On the other hand,dΛ₁₃/Λ₁₃ and dλ₃/λ₃ can implement 10⁻⁷ by using the Fabry-Perot etalon108 and the gas cell 164. Hence, the first term on the left-hand side isthe constraint of equation (25). In addition, if dφ/2π is about 10⁻⁴[wave], inequality (25) can be satisfied by selecting the firstreference wavelength λ₁ such that Λ₁₃ becomes 1.5 mm.

Under the above-described conditions, D/Λ₁₃ is 10³ in inequality (26).Hence, for dΛ₁₂/Λ₁₂, the essential condition is about 10⁻⁴. Hence, thesynthetic wavelength accuracy can be relaxed by two digits, as comparedto the first embodiment. The maximum value of Λ₁₂ necessary under theabove-described conditions is about 1.5 m. When this is converted intothe wavelength difference (wavelength change amount) between the firstreference wavelength λ₁ and the second reference wavelength λ₂, a verysmall value of 1.5 pm is obtained.

In this embodiment, to stabilize the first reference wavelength λ₁ andthe second reference wavelength λ₂ to the transmission spectrum of theFabry-Perot etalon 108, a frequency interval FSR of the Fabry-Perotetalon 108 needs to be smaller in accordance with the above-describedwavelength change amount. If the above-described accuracy of dΛ₁₂/Λ₁₂can be implemented without stabilizing the reference wavelengths to thetransmission spectrum of the Fabry-Perot etalon 108, the secondreference wavelength λ₂ need not be stabilized by the Fabry-Perot etalon108. In this case, since the accuracy of the synthetic wavelength Λ₁₂ isguaranteed by current modulation or temperature modulation, wavelengthchange by the above-described minimum value of the wavelength changeamount is implemented. Note that to implement large wavelength change bythe DFB-DL, temperature modulation is necessary, and wavelength changetakes a long time. However, when the wavelength change amount isdecreased, as described above, high-speed wavelength change canadvantageously be implemented by current modulation.

In step S1118, the environment in the space near the test surface TS,that is, between the reference surface RS and the test surface TS isdetected, as in step S216.

In step S1120, the phase detection unit 172 b detects the phase φ₃ atthe third reference wavelength λ₃.

In step S1122, the refractive index (atmospheric refractive index) inthe space between the reference surface RS and the test surface TS iscalculated, thereby obtaining the absolute distance D between thereference surface RS and the test surface TS. More specifically, theabsolute distance D is obtained in accordance with equation (22)described above. However, especially when the absolute distance D is tobe obtained after executing order-of-interference determinationprocessing, the absolute distance D (absolute distance D₃) is obtainedby

$\begin{matrix}{D = {\frac{\lambda_{3}}{2{n\left( \lambda_{3} \right)}}\left( {{{round}\left( {{\frac{n\left( \lambda_{3} \right)}{n_{g}\left( {\lambda_{1},\lambda_{3}} \right)}\frac{\Lambda_{13}}{\lambda_{3}}\left( {{{round}\left( {{\frac{n_{g}\left( {\lambda_{1},\lambda_{3}} \right)}{n_{g}\left( {\lambda_{1},\lambda_{2}} \right)}\frac{2D_{1}}{\Lambda_{13}}} - \frac{\phi_{3} - \phi_{1}}{2\pi}} \right)} + \frac{\phi_{3} - \phi_{1}}{2\pi}} \right)} - \frac{\phi_{3}}{2\pi}} \right)} + \frac{\phi_{3}}{2\pi}} \right)}} & (27)\end{matrix}$

Step S1124 is the same as step S222, and a detailed description thereofwill not be repeated here.

As described above, according to the measuring apparatus 1C of thisembodiment, the wavelength change amount and wavelength change accuracycan be reduced. It is therefore possible to accurately measure theabsolute distance between the reference surface RS and the test surfaceTS using a simple arrangement without requiring a referenceinterferometer.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent application No.2009-254452 filed on Nov. 5, 2009, which is hereby incorporated byreference herein in its entirety.

What is claimed is:
 1. A measuring apparatus for measuring an absolutedistance between a reference surface and a test surface, the measuringapparatus comprising: a first light source; a wavelength referenceelement configured to set a wavelength of light to be emitted by thefirst light source to one of a first reference wavelength that is aknown vacuum wavelength or a second reference wavelength that is a knownvacuum wavelength different from the first reference wavelength; apolarizing beam splitter configured to split the light from the firstlight source into light having a first polarization direction and lighthaving a second polarization direction perpendicular to the firstpolarization direction, make the light having the first polarizationdirection enter the reference surface, and make the light having thesecond polarization direction enter the test surface; a refractive indexdetection unit configured to detect a group index in a space between thereference surface and the test surface; a phase detection unitconfigured to detect an interference signal between the light having thefirst polarization direction and reflected by the reference surface andthe light having the second polarization direction and reflected by thetest surface, and detect, from the interference signal, a phasecorresponding to an optical path length between the reference surfaceand the test surface; and a processing unit configured to performprocessing of obtaining the absolute distance by controlling said phasedetection unit so as to detect the phase corresponding to the opticalpath length between the reference surface and the test surface for eachof the first reference wavelength and the second reference wavelengthwhile changing the wavelength of light to be emitted by the first lightsource continuously from the first reference wavelength to the secondreference wavelength by using said wavelength reference element, whereinletting λ₁ be the first reference wavelength, λ₂ be the second referencewavelength, φ₁ be the phase detected by said phase detection unit at thefirst reference wavelength, φ₂ be the phase detected by said phasedetection unit at the second reference wavelength, M be the number ofphase jumps that occur when the wavelength of light to be emitted by thefirst light source is continuously changed from the first referencewavelength to the second reference wavelength, Λ_(l2) be a syntheticwavelength of the first reference wavelength and the second referencewavelength represented by λ₁·λ₂/|λ₁−λ₂|, n_(g) be the group indexdetected by said refractive index detection unit, and k be the number oftimes the test surface reflects the light having the second polarizationdirection, said processing unit obtains the absolute distance D₁ by:${D_{1} = {\frac{1}{2{k \cdot n_{g}}}\left( {M + \frac{\phi_{2} - \phi_{1}}{2\pi}} \right)\Lambda_{12}}},$wherein letting dλ₂ be an error from a designed value of the secondreference wavelength, dΛ_(l2) be an error from a designed value of thesynthetic wavelength of the first reference wavelength and the secondreference wavelength, dφ be a detection error of said phase detectionunit, and n₂ be a refractive index at λ₂, a range Dmax of the absolutedistance measurable by the measuring apparatus satisfies:${{{\sqrt{2}\frac{d\;\phi}{2\pi}\frac{\Lambda_{12}}{\lambda_{2}}} + {\frac{2{k \cdot D_{\max}}}{\lambda_{2}}\frac{d\;\Lambda_{12}}{\Lambda_{12}}} + {\frac{2{k \cdot D_{\max}}}{\lambda_{2}}\frac{d\;\lambda_{2}}{\lambda_{2}}}} < \frac{1}{2}},{and}$said processing unit obtains the absolute distance D₂ by:$D_{2} = {\frac{\lambda_{2}}{2{k \cdot n_{2}}}{\left( {{{round}\left( {\frac{2{k \cdot D_{1}}}{\lambda_{1}} - \frac{\phi_{1}}{2\pi}} \right)} + \frac{\phi_{1}}{2\pi}} \right).}}$2. The apparatus according to claim 1, further comprising: a shifterconfigured to shift a frequency of the light having the firstpolarization direction and reflected by the reference surface; and achange unit configured to change the polarization direction of the lighthaving the first polarization direction and having passed through saidshifter, wherein said phase detection unit includes a light amountdetector configured to detect the interference signal between the lighthaving the first polarization direction and reflected by the referencesurface and the light having the second polarization direction andreflected by the test surface.
 3. The apparatus according to claim 1,wherein said phase detection unit includes: a phase difference addingunit configured to add a plurality of known phase differences to each ofthe light having the first polarization direction and the light of thesecond polarization direction; and a plurality of light amount detectorseach configured to detect an interference signal for the plurality ofknown phase differences added by said phase difference adding unit. 4.The apparatus according to claim 1, wherein said wavelength referenceelement includes a Fabry-Perot etalon.
 5. The apparatus according toclaim 1, wherein said wavelength reference element includes a gas cellhaving an absorption line at the known vacuum wavelength.
 6. Theapparatus according to claim 1, wherein said refractive index detectionunit includes: a thermometer configured to detect a temperature in thespace between the reference surface and the test surface; and ahygrometer configured to detect an atmospheric pressure in the spacebetween the reference surface and the test surface.
 7. The apparatusaccording to claim 1, wherein said refractive index detection unitincludes: a third light source configured to emit light having awavelength different from the wavelength of the light from the firstlight source; and a detection unit configured to detect, using the lightfrom said third light source, an optical path difference between thereference surface and the test surface in the same optical path as thatof the light from the first light source.
 8. The apparatus according toclaim 1, wherein said refractive index detection unit includes adetection unit configured to detect an interference signal correspondingto an optical path difference between a first optical path of vacuumatmosphere having a known length and a second optical path of atmospherehaving the same length as that of the first optical path.
 9. A measuringapparatus for measuring an absolute distance between a reference surfaceand a test surface the measuring apparatus comprising: a first lightsource; a wavelength reference element configured to set a wavelength oflight to be emitted by the first light source to one of a firstreference wavelength that is a known vacuum wavelength or a secondreference wavelength that is a known vacuum wavelength different fromthe first reference wavelength; a polarizing beam splitter configured tosplit the light from the first light source into light having a firstpolarization direction and light having a second polarization directionperpendicular to the first polarization direction, make the light havingthe first polarization direction enter the reference surface, and makethe light having the second polarization direction enter the testsurface; a refractive index detection unit configured to detect a groupindex in a space between the reference surface and the test surface; aphase detection unit configured to detect an interference signal betweenthe light having the first polarization direction and reflected by thereference surface and the light having the second polarization directionand reflected by the test surface, and detect, from the interferencesignal, a phase corresponding to an optical path length between thereference surface and the test surface; a processing unit configured toperform processing of obtaining the absolute distance by controllingsaid phase detection unit so as to detect the phase corresponding to theoptical path length between the reference surface and the test surfacefor each of the first reference wavelength and the second referencewavelength while changing the wavelength of light to be emitted by thefirst light source continuously from the first reference wavelength tothe second reference wavelength by using said wavelength referenceelement; a second light source configured to emit light having a thirdreference wavelength different from the first reference wavelength andthe second reference wavelength, wherein letting λ₁ be the firstreference wavelength, λ₂ be the second reference wavelength, φ₁ be thephase detected by said phase detection unit at the first referencewavelength, φ₂ be the phase detected by said phase detection unit at thesecond reference wavelength, M be the number of phase jumps that occurwhen the wavelength of light to be emitted by the first light source iscontinuously changed from the first reference wavelength to the secondreference wavelength, Λ_(l2) be a synthetic wavelength of the firstreference wavelength and the second reference wavelength represented byλ₁·λ₂/|λ₁−λ₂|, n_(g) be the group index detected by said refractiveindex detection unit, and k be the number of times the test surfacereflects the light having the second polarization direction, saidprocessing unit obtains the absolute distance D₁ by:${D_{1} = {\frac{1}{2{k \cdot n_{g}}}\left( {M + \frac{\phi_{2} - \phi_{1}}{2\pi}} \right)\Lambda_{12}}},$wherein said polarizing beam splitter splits the light from the secondlight source into light having the first polarization direction andlight having the second polarization direction, makes the light havingthe first polarization direction enter the reference surface, and makesthe light having the second polarization direction enter the testsurface, wherein said processing unit controls said phase detection unitso as to detect the phase corresponding to the optical path lengthbetween the reference surface and the test surface for the thirdreference wavelength, wherein letting λ₃ be the third referencewavelength, φ₃ be the phase detected by said phase detection unit at thethird reference wavelength, Λ₁₃ be a synthetic wavelength of the firstreference wavelength and the third reference wavelength represented byλ₁·λ₃/|λ₁−λ₃|, dλ₃ be an error from a designed value of the thirdreference wavelength, dΛ_(l2) be an error from a designed value of thesynthetic wavelength of the first reference wavelength and the secondreference wavelength, dΛ₁₃ be an error from a designed value of thesynthetic wavelength of the first reference wavelength and the thirdreference wavelength, dφ be a detection error of said phase detectionunit, and n₃ be a refractive index at λ₃, a range Dmax of the absolutedistance measurable by the measuring apparatus satisfies:${{{\sqrt{2}\frac{d\;\phi}{2\pi}\frac{\Lambda_{13}}{\lambda_{3}}} + {\frac{2{k \cdot D_{\max}}}{\lambda_{3}}\frac{d\;\Lambda_{13}}{\Lambda_{13}}} + {\frac{2{k \cdot D_{\max}}}{\lambda_{3}}\frac{d\;\lambda_{3}}{\lambda_{3}}}} < \frac{1}{2}};{and}$${{{\sqrt{2}\frac{d\;\phi}{2\pi}\frac{\Lambda_{12}}{\Lambda_{13}}} + {\frac{2{k \cdot D_{\max}}}{\Lambda_{13}}\frac{d\;\Lambda_{12}}{\Lambda_{12}}} + {\frac{2{k \cdot D_{\max}}}{\Lambda_{13}}\frac{d\;\Lambda_{13}}{\Lambda_{13}}}} < \frac{1}{2}},{and}$wherein said processing unit obtains the absolute distance D₃ by:$D_{3} = {\frac{\lambda_{3}}{2{k \cdot n_{3}}}{\left( {{{round}\left( {{\frac{\Lambda_{13}}{\lambda_{3}}\left( {{{round}\left( {\frac{2{k \cdot D_{1}}}{\Lambda_{13}} - \frac{\phi_{3} - \phi_{1}}{2\pi}} \right)} + \frac{\phi_{3} - \phi_{1}}{2\pi}} \right)} - \frac{\phi_{3}}{2\pi}} \right)} + \frac{\phi_{3}}{2\pi}} \right).}}$10. The apparatus according to claim 9, further comprising: a shifterconfigured to shift a frequency of the light having the firstpolarization direction and reflected by the reference surface; and achange unit configured to change the polarization direction of the lighthaving the first polarization direction and having passed through saidshifter, wherein said phase detection unit includes a light amountdetector configured to detect the interference signal between the lighthaving the first polarization direction and reflected by the referencesurface and the light having the second polarization direction andreflected by the test surface.
 11. The apparatus according to claim 9,wherein said phase detection unit includes: a phase difference addingunit configured to add a plurality of known phase differences to each ofthe light having the first polarization direction and the light of thesecond polarization direction; and a plurality of light amount detectorseach configured to detect an interference signal for the plurality ofknown phase differences added by said phase difference adding unit. 12.The apparatus according to claim 9, wherein said wavelength referenceelement includes a Fabry-Perot etalon.
 13. The apparatus according toclaim 9, wherein said wavelength reference element includes a gas cellhaving an absorption line at the known vacuum wavelength.
 14. Theapparatus according to claim 9, wherein said refractive index detectionunit includes: a thermometer configured to detect a temperature in thespace between the reference surface and the test surface; and ahygrometer configured to detect an atmospheric pressure in the spacebetween the reference surface and the test surface.
 15. The apparatusaccording to claim 9, wherein said refractive index detection unitincludes: a third light source configured to emit light having awavelength different from the wavelength of the light from the firstlight source; and a detection unit configured to detect, using the lightfrom said third light source, an optical path difference between thereference surface and the test surface in the same optical path as thatof the light from the first light source.
 16. The apparatus according toclaim 9, wherein said refractive index detection unit includes adetection unit configured to detect an interference signal correspondingto an optical path difference between a first optical path of vacuumatmosphere having a known length and a second optical path of atmospherehaving the same length as that of the first optical path.